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Fractions, Decimals, and PercentsThe BMX rider in the picture is one quarter of the way through a race course.Her time at this point is 4 min, 52.9 s.When training in hot weather, riders need to make sure they keep up their ﬂuid levels.Losing 4 to 5 percent of body mass through sweat can seriously decrease a rider’sperformance. Further dehydration may cause illness.Fractions, decimals, and percents are used in many sports, as well as in other aspects of dailylife. When you get a test score back, you might change it to a percent so you can compare itto your other test results. You often think of money in both decimals and fractions. Forexample, 1.25 is one whole dollar plus a quarter.In this chapter, you will learn how fractions, decimals, and percents are related and usethem to solve problems.What You Will Learnφto compare and order fractions, decimals,and percentsφto convert among fractions, decimals, andpercentsφto relate fractions to terminating orrepeating decimal numbersφto solve problems involving percentsKey Wordspercentrepeating decimalterminating decimalMATH LINKHow are fractions, decimals, and percentsused in the media? Start collectingnewspaper headlines, articles, andadvertisements that show diﬀerent waysto use fractions, decimals, and percents.122NEL Chapter 4esHeadlin%rops by 1 GST D Young 7 OutDerby Wrticipateents Paf 10 Studoainbow.65 kg Rtches 2inner Cain FundTroutRaising

;DA967A:H /-ÌÕ ÞÊ/ Make the following Foldable to organizewhat you learn in Chapter 4.Step 1 Collect three sheets of paper andplace them 2 cm apart. Keep theedges straight.Step 2 Fold the bottom edge of thepaper. Stop 2 cm from the topedge. This makes all tabs thesame size. Staple together alongthe fold.Step 3 Label the tabs.Chapter 4: Fractions, Decimals, and PercentsKey Words4.14.24.3What I Need to Work OnLiteracyLinkAs you work through Chapter 4, takenotes under the appropriate tab.Include information about the keywords, examples, and key ideas.ChapterChapter 4 NEL123

Connect Fractions, Decimals,and PercentsFocus on After this lesson, youwill be able to φ estimate percentsφφas fractions or asdecimalscompare andorder fractions,decimals, andpercentsestimate andsolve problemsinvolving percentpercent means “out of 100” 30% means 30 out of30 or 0.30.100 or100Kim likes to do research on the Internet before he travels. He has founda video of orcas, or killer whales, migrating off the coast of BritishColumbia. The video is 20 megabytes, and 25% has alreadydownloaded. How many megabytes is that?How can you estimate percents? cardboard or index cardrulerscissors25-cm length of ribbonor paper strip (at least1 cm wide)felt markertape124NEL Chapter 4You can use a visual model like an Internet loading strip to help makereasonable estimates of percent and corresponding number values.1.Cut a piece of index card orcardboard to make a rectangle thatis 5 cm by 12 cm. Cut a slot 1.5 cmin from each end of your cardboard.Make each slot slightly longer thanthe width of the ribbon or paperstrip you will use in step 3.12 cm5 cm

Use your money skills to think about fractions, decimals, and percents. 0.251 of a dollar425% of a dollar 0.10 0.501 of a dollar250% of a dollar1 of a dollar1010% of a dollarExample 1: Find a Percent of a NumberFour brothers bought their mother a birthday present for 84.60.They each paid 25% of the bill. How much was each brother’s share?b) Ten co-workers are buying Ted a going away present and will eachpay 10%. They decide to buy him a backpack for 92.30, includingtax. How much should each pay?a) 84.60 2 42.30Solutiona) Find 50% of 84.60.50% of 84.60 is half of 84.60.Half of 84.60 is 42.30.Now find 25% of 84.60.25% is half of 50%.Half of 42.30 is 21.15. 42.30 2 21.15So, 25% of 84.60 is 21.15.Check: 21.15 4 84.60Each brother’s share is 21.15.1.25% is also4I could havedivided by 4. 84.60 4 21.15b)Find 10% of 92.30.10Recall that 10% 1001 1010% of 92.30 is one tenth of 92.30.One tenth of 92.30 is 9.23.Each co-worker should pay 9.23.a)b)c)126NEL Chapter 4Find 50% of 45.80.Find 25% of 50.00.Find 10% of 72.40.0%50%100%0? 84.600%25%50%100%0? 42.30 84.60 92.30 10 9.23

Example 2: Find the Percent of a Number MentallyWhat is 75% of 80?SolutionMethod 1: Use Percents You Know50% of 80 is half of 80.Half of 80 is 40.25% is half of 50%.Half of 40 is 20.75% is 50% 25%.0%25%50%0204075% 100%?8075% of 80 40 20 60So, 75% of 80 is 60.Method 2: Think of a Model80 is., so divide the blocks into 4 groups.75% is 34Each group has, or 20.StrategiesWhat other methodcould you use?Count the number of blocks in 3 groups.Three groups will have 3 20 or 60.So, 75% of 80 is 60.Use mental math to find each percent.a) 75% of 16b) 60% of 90c) 40% of 804.1 Connect Fractions, Decimals, and Percents NEL127

A iZgVXnExample 3: Compare Fractions, Decimals, and PercentsA c 3, 70%, and 0.72. Write them in ascending order.Compare4Ascending ordermeans from least togreatest.SolutionExpress all three values in decimal form.3is 0.75.470% is 0.700.72 is 0.72Compare 0.75, 0.70, and 0.72.0.70 0.72 0.75Descending ordermeans from greatestto least.So, 70% 0.72 34Compare place values.Look at the hundredths place.70% 0.7203410.5Write each set of numbers in ascending order using the symbol.39 , 0.36a) 56%, 0.48, 1b) 35%,2100 A visual model can help you solve problems involving percents. Every percent has an equivalent decimal and fraction value.50%25%10%25% is 0.25 or 1450% is 0.50 or 12110% is 0.10 or10 You can use place value or a number line to comparefractions, decimals, and percents.11 is between 45% and 0.53.45% 2 0.5321 0.5345% 200.5128NEL Chapter 445% is 0.451 is 0.521

How could you find 60% of 120? Explain using diagrams or aloading-strip model.b) Can you find 60% of 120 in more than one way? Explain.1. a)Your friend missed the lesson on understanding how to find 25% of anumber. Explain at least two ways to visualize or understand 25%.b) Show your friend how to find 12.5% of a number.2. a)3.You know how to mentally find 10% and 25% of a number. Write at leastthree other percent amounts you could find using that knowledge.4.How could you mentally find 1% of a number?For help with #9 to #11, refer to Example 2 onpage 127.For help with #5 to #8, refer to Example 1 onpage 126.5.What is 50% of each quantity?a) 134 marblesb) 46 cookiesc) 74.80d) 65.4 m6.What is 25% of each quantity?a) 68 daffodilsb) 7.2 cmc) 42 mind) 0.567.What is 10% of each quantity?a) 15 minb) 34 cmc) 50 catsd) 89.508.Show how to find each amount.a) 50% of 44b) 25% of 20c) 10% of 12d) 1% of 1509.Show how to find eachamount mentally.a) 60% of 40b) 75% of 44c) 20% of 750d) 35% of 24010.Show how to find eachamount mentally.a) 75% of 60b) 35% of 120 mc) 85% of 280 studentsd) 30% of 45 cm11.Describe how you could find 37.5% of 68using only the ability to divide in half andto perform addition. Show your numbersfor each step.4.1 Connect Fractions, Decimals, and Percents NEL129

For help with #12 to #18, refer to Example 3 onpage 128.12.Change each percent to a decimal number.a) 42%b) 38%c) 15% d) 73%14.Compare the numbers in each set. Writethem in ascending order.1 , 0.1214%,1041 , 40%, 0.39c)100a)b)03 , 0.3532%,10, 45%, 0.54c) 12b)76%, 0.72, 34Use the number line to help answer thequestions below.025%50%75%20.According to an article in the newspaper,35% of Regina residents like winter. If thepopulation of Regina is 178 000, howmany people like winter? Show twodifferent ways to find the answer.21.Your bill at a restaurant is 28. You wantto leave a 15% tip. How could youcalculate the amount mentally?22.Carey found that35% of the studentsin her school readfantasy books. Ifthere are 840students in theschool, how manystudents readfantasy books?23.John’s mass was 62 kg last year. If hismass increased by 10% this year, whatis his current mass?24.Three years ago,Sam’s height was108 cm. Since thattime he has grown25% in height.a) How much hashe grown?b) How tall is henow?a)17.On each number line, which number iscorrectly placed? How do you know?a)27.3 28.5 3126b)3015780130NEL Chapter 4340.18122In Australia, the GST is 10%. How wouldyou estimate the GST on items you mightbuy on holiday in Australia?100%What is a fraction between 25% and50%? How do you know?b) What is a decimal number between 0%and 25%?c) What is a decimal number between 75%and 100% that is closer to 75%?119.Compare the numbers in each set. Writethem in descending order.a)16.1, 0.2427%,4What decimal number could be placed atA on the number line? Justify your answer.AChange each percent to a decimal number.a) 57%b) 30%c) 5%d) 88%13.15.18.

Fractions, Decimals, and PercentsFocus on After this lesson, youwill be able to φ convert amongφφφfractions, decimals,and percentsestimate percentvaluesdistinguishbetweenterminating andrepeating decimalsrelate fractions toterminating andrepeating decimalsIndividual statistics from sporting events are often reported as percentsor decimal numbers. It may be necessary to convert among fractions,decimals, and percents to better understand these statistics.How can you convert among fractions, decimals, andpercents?1.SportsLinkAlthough the statisticis called “savepercentage,” theresult is a decimalnumber.132NEL Chapter 42.Look at the statistics inthe table. Which hockeygoalie do you think ishaving the best season?Why?GoalieShots on GoalSavesA. Auld673606M. Fernandez586545M. Kiprusoff797726D. Hasek709658Goalies can be rated on “save percentage.” This statistic is the ratioof saves to shots on goal.Number of savesSave percentage Shots on goala)Copy the table into your notebook. Extend the table to includetwo more columns.

Solutiona) Total games wins lossesMiami:Total games 59 23 82Team percentage 5982New Jersey:Total games 42 40 8242Team percentage 82Los Angeles:Total games 34 48 82Team percentage 3482b) Convert each fraction to a decimal.Miami:59 0.720C 59 82 0.719512191.820.71950.719New Jersey:42 0.512820.720C 42 82 0.512195121.0.51210.512Los Angeles:34 0.415820.513C 34 82 0.414634146.0.41460.414c)0.415NEL Chapter 4The digit to the right ofthe thousandths placeis 1, so round down.The digit to the right ofthe thousandths placeis 6, so round up.To convert to a percent, multiply the decimal by 100.Miami team percentage 0.72 100% 72%New Jersey team percentage 0.512 100% 51.2%Los Angeles team percentage 0.415 100% 41.5%134The digit to the rightof the thousandthsplace is 5, so round up.

Convert each fraction to a decimal number. Round each decimalnumber to the indicated place value. Then, convert to a percent.27 (tenths) b)125 (thousandths) c)1496 (hundredths)a)563962005Example 2: Change Fractions to Repeating DecimalsSome common fractions may change to repeating decimal numbers.These decimal numbers contain one or more digits that repeat overand over without ending.Use a calculator to change each fraction to a repeating decimal.a) 1b) 5c) 5396Solution1 1 3a)3 0.3repeating decimal a decimal number witha digit or group ofdigits that repeatsforever repeating digits areshown with a bar,e.g., 0.777 0.7C 1 3 0.333333333Use a bar over the 3 toshow the repeating part.b) 59 5 9The calculator shows the ﬁnaldigit as 6 because it roundsup. It would show more 5s if ithad a larger display.C 5 9 0.555555556 0.5c)5 5 66C 5 6 0.833333333 0.83Place a bar over only the 3since the 8 does not repeat.Show the following fractions as repeating decimals.2 b) 7a)394.2 Fractions, Decimals, and Percents NEL135

Example 3: Estimate PercentsPaige has answered 94 questions correctly out of 140 questions.Estimate her mark as a percent.SolutionThink: What is 50% of 140?Half of 140 is 70.0%Think: What is 10% of 140?140 10 14StrategiesGuess and CheckRefer to page xvi.60%50% 70%100%70 84 9894140Add 50% and 10% parts together to estimate.50% 10% 60% of 14070 14 84Too low.50% 10% 10% 70% of 14070 14 14 98Too high.The answer is between 60% and 70% but closer to 70%.Estimate each of the following as a percent.a) 23 out of 80b) 421 out of 560Example 4: Change Terminating Decimal Numbers to Fractionsa)b)terminating decimal a decimal number inwhich the digits stop examples include 0.4,0.86, 0.125What fraction of a dollar is 0.75?Change 0.652 to a fraction.Solutiona) The decimal number 0.75 is a terminating decimal . The last digit isin the hundredths place, so the denominator is 100.750.75 0.75 is 75 1003 of a dollar.75 of a dollar orSo, 0.75 is1004b)The 2 is in the thousandths place, so thedenominator is 1000.6520.652 1000Change each terminating decimal number to a fraction.a) 0.48b) 0.078136NEL Chapter 43 quarters

7.A baseball player’s batting average is theratio of number of hits to times at bat. It isusually expressed as a decimal number.of hitsBatting average NumberTimes at batThe following data arefor one baseball season.PlayerTimes at BatHitsA605194B624197What is the batting average for eachplayer? Round each answer to thenearest thousandth.b) Which player had a better battingaverage for the season? Justify yourresponse.a)For help with #12 and #13, refer to Example 3 onpage 136.12.Estimate each of the followingas a percent.a) 36 out of 70b) 125 out of 30013.Estimate each of the followingas a percent.a) 275 out of 500b) 46 out of 90For help with #14 and #15, refer to Example 4 onpage 136.14.Change each decimal number to a fraction.a)15.0.95b)0.3c)0.243d)0.08Change each decimal numbers to a fraction.a) 0.80b) 0.2c) 0.18d) 0.455For help with #8 to #11, refer to Example 2 onpage 135.8.Write each repeating decimal numberusing bar notation.a) 0.5555555 b) 0.090909 c) 0.1877777 d) 2.0151515 9.Write each repeating decimal numberusing bar notation.a) 0.4444444 b) 0.2666666 c) 0.1851851 d) 1.0626262 10.Change each fraction to a repeatingdecimal. Then use bar notation to showthe repeating part.5a)611.345c)997d)11Change each fraction to a repeatingdecimal. Then use bar notation to showthe repeating part.1a)6138b) 2b) 37NEL Chapter 425c)994d)1116.Express the value of each coin as afraction of a dollar. Write the fractionsin ascending order.b) Express the value of each coin as adecimal number. Write the decimalnumbers in ascending order.c) Write a statement using percent thatcompares the three coins.a)17.For each of the following statements,rewrite each percent or decimal as afraction.a) 0.71 of Earth’s surface is coveredwith water or ice.b) Matthew’s batting average is .421.c) Nitrogen makes up approximately78% of the air we breathe.